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Cluster state plays a crucial role in the one-way quantum computation. Here,we propose and experimentally demonstrate a new scheme to prepare anultrahigh-fidelity four-photon linear cluster state via spontaneous parametricdown-conversion process. The state fidelity is measured to be$0.9517\pm0.0027$. Our scheme can be directly extended to more photons togenerate N-qubit linear cluster state. Furthermore, our scheme is optimal forgenerating photonic linear cluster states in the sense of achieving the maximalsuccess probability and having the simplest strategy. The key idea is that thephoton pairs are prepared in some special non-maximally entangled statesinstead of the normal Bell states. To generate a 2N-qubit linear cluster statefrom N pairs of entangled photons, only (N-1) Hong-Ou-Mandel interferences areneeded and a success probability of $(\frac{1}{4})^{N-1}$ is achieved.

Experimental generation of a high-fidelity four-photon linear cluster state